Question 2: A circular drum of radius of 40 cm is initially rotating at 400 revolutions/min. It is brought to stop after making 50 revolution. What is the angular acceleration and the stopping time?

Explanation: We are given the initial angular velocity of the drum, 400 revolutions/min. Some opposite force is applied to stop the revolution of the drum. As the drum comes to stop, therefore, the final angular velocity is 0 rev/min. Similarly, the angular displacement before stopping is 50 revolution. We have to find the angular acceleration (off course it is negative angular acceleration) and the time in which drum stops (before taking the 50 revolutions.

Now for one revolution, the angular displacement is θ = 360° = 2π radian. Therefore, the angular displacement covered before stopping = 50 revolutions = 50 × 2π rad.

Note: All equations of motion in linear motion have their corresponding equations in circular motion. For, 2as = v_{f}^{2} – v_{i}^{2}, the corresponding equation in rotatory motion is 2αθ = ω_{f}^{2} – ω_{i}^{2}. For v_{f} = v_{i} + at, the corresponding equation in circular motion is ω_{f} = ω_{i} + αt

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Excellent , I appreciate it very much thanks

Muhib UllahThank you very much.

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